Rút gọn biểu thức sau:

Đáp án:

`A = 10/x`

Giải thích các bước giải:

`A = ((5x + 2)/(x^2 - 10x) + (5x - 2)/(x^2 + 10x)) . (x^2 - 100)/(x^2 + 4)`

`= ((5x + 2)/(x(x - 10)) + (5x - 2)/(x(x + 10))) . (x^2 - 10^2)/(x^2 + 4)`

`= (((5x + 2)(x + 10))/(x(x - 10)(x + 10)) + ((5x - 2)(x - 10))/(x(x - 10)(x + 10))). ((x - 10)(x + 10))/(x^2 + 4)`

`= (((5x + 2)(x + 10) + (5x - 2)(x - 10))/(x(x -10)(x + 10))) . ((x - 10)(x + 10))/(x^2 + 4)`

`= ((5x^2 + 50x + 2x + 20 + 5x^2 - 50x - 2x + 20)/(x(x - 10)(x + 10))) .((x - 10)(x + 10))/(x^2 + 4)`

`= (10x^2 + 40)/(x(x - 10)(x + 10)) .((x - 10)(x + 10))/(x^2 + 4)`

`= (10(x^2 + 4))/(x(x - 10)(x + 10)) .((x - 10)(x + 10))/(x^2 + 4)`

`= 10/x`

Vậy `A = 10/x`